Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-x-2y &= -9 \\ 2x+2y &= 9\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $x = 0$ $x = 0$ Substitute $0$ for $x$ in the top equation. $- 0-2y = -9$ $-2y = -9$ $-2y = -9$ $y = \dfrac{9}{2}$ The solution is $\enspace x = 0, \enspace y = \dfrac{9}{2}$.